Which of the following numbers is a multiple of 5? ${41,51,63,65,104}$
Answer: The multiples of $5$ are $5$ $10$ $15$ $20$ ..... In general, any number that leaves no remainder when divided by $5$ is considered a multiple of $5$ We can start by dividing each of our answer choices by $5$ $41 \div 5 = 8\text{ R }1$ $51 \div 5 = 10\text{ R }1$ $63 \div 5 = 12\text{ R }3$ $65 \div 5 = 13$ $104 \div 5 = 20\text{ R }4$ The only answer choice that leaves no remainder after the division is $65$ $ 13$ $5$ $65$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $5$ are contained within the prime factors of $65$ $65 = 5\times13 5 = 5$ Therefore the only multiple of $5$ out of our choices is $65$. We can say that $65$ is divisible by $5$.